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Covering the Baire space by families which are not finitely dominating

Heike Mildenberger, Saharon Shelah, Boaz Tsaban

Published 2004-07-28, updated 2010-10-31Version 4

It is consistent (relative to ZFC) that the union of max{b,g} many families in the Baire space which are not finitely dominating is not dominating. In particular, it is consistent that for each nonprincipal ultrafilter U, the cofinality of the reduced ultrapower w^w/U is greater than max{b,g}. The model is constructed by oracle chain condition forcing, to which we give a self-contained introduction.

Comments: Small updates
Journal: Annals of Pure and Applied Logic 140 (2006), 60--71
Categories: math.LO, math.CO, math.GN
Subjects: 03E15, 03E17, 03E35, 03D65
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